Turbulent flame speed and self-similar propagation of expanding premixed flames

A unified scaling of experimental turbulent flame speed data, measured in constant-pressure expanding turbulent premixed flames, propagating in nearly homogenous isotropic turbulence in a dual-chamber fan-stirred vessel is presented. While the cold flow is characterized by high speed particle image velocimetry, the flame propagation rate is obtained by tracking high speed Schlieren images of unity Lewis number methane-air flames over wide ranges of pressure and turbulence intensity. It is found that the normalized turbulent flame speed as a function of the average radius scales as a turbulent Reynolds number to the one-half power, where the average radius is the length scale and thermal diffusivity is the transport property, thus showing self-similar propagation. Utilizing this dependence and recent theoretical results obtained by the spectral closure of the G-equation, it is found that the turbulent flame speeds from expanding flames and those from Bunsen geometries are scaled by the same one half power dependency of the turbulent Reynolds number with appropriate choice of length scales.